Look if ULN2803 to see if it fits your needs.
No good with common anode display. red913 needs a high-side switch for each digit, if I understand/guess correctly.
Normally a high-side switch (meaning between the positive supply and the component being switched) is done with a pnp transistor (for example bc327). A base resistor would be needed eg. 4K7.
Paul__B's suggestion of using an npn as an emitter follower also works and has the advantage of not needing a base resistor (the base current is naturally limited in this configuration).
The disadvantage of npn as emitter follower is that it drops quite a lot of the supply voltage (0.7V or more). As Paul__B says, with red or green displays, which have a low forward voltage (around 2~2.5V), this won't be a problem.
With blue or white displays (rare) the forward voltage is higher (up to 3.5V) and they may not work with the emitter followers, as there might not be quite enough remaining voltage from 5V to drive them, even with very low series resistors (must not leave those out!). The pnp would have an advantage here because they will only drop around 0.3V.
If you connect the npn to 9V as Paul__B suggested, you won't have any more voltage than if you connected to 5V, so still can't run blue/white displays. (For that you would have to use PNPs as high-side switches, with NPNs to switch the PNPs on.) But at least you could run your displays directly from the 9V supply, avoiding that load on the Arduino's regulator.
Previous paragraph heavily edited following advice and corrections from Paul__B!Paul